{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Image of Charge Above Plane

\n", "\n", "\"\"\" From \"COMPUTATIONAL PHYSICS\" & \"COMPUTER PROBLEMS in PHYSICS\"\n", " by RH Landau, MJ Paez, and CC Bordeianu (deceased)\n", " Copyright R Landau, Oregon State Unv, MJ Paez, Univ Antioquia, \n", " C Bordeianu, Univ Bucharest, 2020. \n", " Please respect copyright & acknowledge our work.\"\"\"\n", "\n", "

\n", " The method of image charges is used to compute potential of a charge above conducting plane." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# ImagePlane.py: potential of charge above conducting plane via images\n", " \n", "import numpy as np, matplotlib.pyplot as plt\n", "from matplotlib.patches import Circle\n", " \n", "Nx = 50; Ny = 50 # x,y 50 grid\n", "x = np.linspace(-5,5,Nx); y = np.linspace(-5,5,Ny)\n", "X,Y = np.meshgrid(x,y) # Transform coordinates\n", "Ex = np.zeros((Nx,Ny)); Ey = np.zeros((Nx,Ny)) # Ex,Ey(x,y)\n", "\n", "def E(xx,x,y): # E due to charge q at xx\n", " r = np.sqrt(x**2+y**2) # Distance\n", " dm = (x-xx) # Position q to xx\n", " d1 = np.sqrt((dm**2+y**2)) # Position q to x \n", " dp = (x+xx) # x component q\n", " d2 = np.sqrt((dp**2+y**2)) # Distance -q to (x,y)\n", " Ex = dm/d1**3-dp/d2**3 \n", " Ey = y/d1**3 -y/d2**3 \n", " return Ex,Ey \n", " \n", "Ex,Ey = E(2.5,X,Y)\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "circle1 = plt.Circle((2.5, 0),0.2, color='r')\n", "circle2 = plt.Circle((-2.5, 0),0.2, color='b')\n", "ax.add_artist(circle1)\n", "ax.add_artist(circle2)\n", "ax.streamplot(x,y,Ex,Ey)\n", "ax.set_aspect('equal')\n", "ax.set_title('E Field Due to Charge Left of Plane (Red Image)')\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('y')\n", "l = plt.axvline(x=0, linewidth=2, color='g')\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }